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How many integers 100>n>10 are such that, if the

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Manager
Joined: 05 Sep 2007
Posts: 144
Location: New York
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How many integers 100>n>10 are such that, if the [#permalink]  21 Oct 2007, 13:22
How many integers 100>n>10 are such that, if the digits of n are reversed, the resulting integer is n+9?
Director
Joined: 11 Jun 2007
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Re: Integers [#permalink]  21 Oct 2007, 13:41
el1981 wrote:
How many integers 100>n>10 are such that, if the digits of n are reversed, the resulting integer is n+9?

i am probably wrong but i'll take a shot at it:

i get 8 but only by logical thinking (no formulas)

12, 23, 34, 45, 56, 67, 78, 89

in order for it to be n+9, the units and tens digit has be be consecutive (since n + 10 would just be a change in the tens digit 10x)
VP
Joined: 28 Mar 2006
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[#permalink]  21 Oct 2007, 13:53
This is a 2 digit #

any two digit # is of the form 10*x+y

Now its given 10*y + x = 10*x+y + 9 (this is n+9)

So y=x+1

Hence there are 8 numbers

12
23
34
45
56
67
78
89
Manager
Joined: 30 Sep 2007
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[#permalink]  21 Oct 2007, 18:32
Vikram - great formula.
[#permalink] 21 Oct 2007, 18:32
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How many integers 100>n>10 are such that, if the

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